Abstract
A quantum phase model is introduced as a limit for very strong interactions of a strongly correlated q-boson hopping model. The exact solution of the phase model is reviewed, and solutions are also provided for two correlation functions of the model. Explicit expressions, including both amplitude and scaling exponent, are derived for these correlation functions in the low temperature limit. The amplitudes were found to be related to the number of plane partitions contained in boxes of finite size.
Highlights
When quantum groups and strongly interacting boson and fermion systems were topical problems in physics and applied mathematics, Prof
Using the classical MacMahon result of equation (4.2), we find an explicit expression for the leading order term in t−1 of the recurrence correlation function: fK0 e−tH (f†0)K
It can be related to interacting boson systems, quantum optics systems and tight-binding particles hopping on a lattice
Summary
When quantum groups and strongly interacting boson and fermion systems were topical problems in physics and applied mathematics, Prof. Soon it became evident that q-boson type integrable models are related to many mathematical problems They are related to the theory of symmetric functions [7] and to the theory of plane partitions [8,9,10,11,12,13]. Plane partitions (three-dimensional Young diagrams) [7,14,15] were discovered to be connected with amazingly wide ranging problems in mathematics as well as theoretical physics They are intensively studied, e.g. in probability theory [16,17], enumerative combinatorics [18], theory of faceted crystals [19,20], directed percolation [21], theory of random walks on lattices [9,10,15,22] and topological string theory [23]. The results reported for the correlation functions, at the end of §3 and in §5, are new
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